Velocity effects on second order contributions to gravitational frequency shift by a moving Kerr–Newman black hole

The significance of the radial velocity effects on the leading-order gravitational frequency shift in some special cases was reported recently. This paper investigates the gravitational shift of frequency of light propagating in the equatorial plane of a radially moving Kerr–Newman black hole up to the second post-Minkowskian order, and discusses the radial velocity effects on the second-order contributions to the frequency shift. It is found that a new radial velocity effect appears in the second-order Schwarzschild contribution to the frequency shift, in contrast to no radial velocity effect in the first-order contribution, when both the emission and reception events are far away from the lens. Velocity effects on the gravitational frequency shifts induced respectively by the lens's electrical charge and spin are also analyzed.